That may partly be due to the English actors not making convincing Americans, and partly due to the comedic tone of the early episodes, but perhaps mainly because it is narrated using a repetitive song. Fortunately, few RPGs insist that the GM sing out descriptions of events, so we can at least escape that element.
Where & When
Because the gunfight is a famous historical event, this is another serial that we can date precisely: it takes place on the 25th and 26th of October 1881. Most of the story is set in the town of Tombstone in what was then the Arizona Territory of the United States.